Thanks Bill. I think with Hawth's Tools it would be easy enough to create a regular grid of points, offset so they fall in the centre of each grid cell. I've often wondered how ArcGIS treats points that fall between cells, ie right on the border between two. By definition a point has no dimensions, so it can't be said to straddle either cell. But at the same time the raster surface covers the whole area, so I wonder how ArcGIS treats the no-mans-land in between cells. Perhaps they shift the point by an infinitely small amount so that it is then contained within a cell? Interesting thought...

I suspect the 'point on boundary' issue has a lot to do with the units and projections you're using. Here in the UK everything tends to fall rather nicely onto a meter grid. Say you have a 5m raster and you take a bunch of GPS points (at 1m precision), there's a good chance many of those points will end in a 5 or a 0 and will hence straddle multiple cells, or rather straddle no cells depending on how you look at it.

Indeed, if those points are manually input at 10m precision then they're guaranteed to coincide with the corners of raster cells. I suspect it's more common than people think.